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$\sinh (x+y) \cosh (x-y)$ किसके बराबर है?

यदि $x = \sec \phi - \tan \phi$ और $y = \csc \phi + \cot \phi$ है,तो:

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${e^{\log_{10} \tan 1^\circ + \log_{10} \tan 2^\circ + \log_{10} \tan 3^\circ + \dots + \log_{10} \tan 89^\circ}}$ का मान है

यदि $\sin A + \sin B = \frac{1}{2}$ और $\cos A + \cos B = 1$ है,तो $\sin \left(\frac{A-B}{2}\right)$ का मान ज्ञात कीजिए।

मान लीजिए $f_k(x) = \frac{1}{k}(\sin^k x + \cos^k x)$ जहाँ $x \in R$ और $k \ge 1$ है। तो $f_4(x) - f_6(x)$ का मान ज्ञात कीजिए।

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